# Phase 7: Robustness Probes

## Probe 1: Investment/GDP Control (Kopecky-Taylor vs Supply-Side)

| Model | Z₁ | p | R² | N |
|---|---|---|---|---|
| P1-A: Baseline Z → real 10y | 43.724** | 0.0154 | 0.108 | 803 |
| P1-B: Z + gross_investment_gdp → real 10y | 47.979*** | 0.0072 | 0.154 | 803 |
| P1-C: Baseline Z → real 3m | 60.075*** | 0.0043 | 0.005 | 813 |
| P1-D: Z + gross_investment_gdp → real 3m | 55.412*** | 0.0095 | -0.027 | 813 |

## Probe 2: Panel Cointegration

- Engle-Granger: 11/23 countries reject no-cointegration at 5%
- Mean EG t-stat: -3.147
- Kao pooled ADF: t=-13.799 (reject at 5%)
- Unit root (Z_1): 0/237 reject (0%)
- Unit root (real_bond_10y): 0/23 reject (0%)

## Probe 3: Portfolio Equity Outlier Check

| Model | Z₁ | p | R² | N | Countries |
|---|---|---|---|---|---|
| P3-A: Full sample Z → port eq/GDP | -374.47*** | 0.0000 | 0.0483 | 5435 | 174 |
| P3-B: Excl financial ctrs → port eq/GDP | -298.51*** | 0.0000 | 0.0141 | 5248 | 168 |
| P3-C: Winsorized → port eq/GDP | -374.87*** | 0.0000 | 0.0999 | 5435 | 174 |
| P3-D: Drop top 5 → port eq/GDP | -313.98*** | 0.0000 | 0.0971 | 5411 | 173 |

## Probe 4: Housing with GDP per Capita

| Model | old_dep | p | youth_dep | p | R² | N |
|---|---|---|---|---|---|---|
| P4-A: age ratios → Δreal HPI | 6614.2** | 0.030 | 11758.0*** | 0.001 | 0.024 | 851 |
| P4-B: age ratios + log_gdppc → Δreal HPI | 1129.2 | 0.293 | -84.7 | 0.946 | 0.008 | 732 |
| P4-C: lagged age ratios → Δreal HPI | 8349.3** | 0.012 | 11897.9*** | 0.000 | 0.026 | 851 |
| P4-D: lagged age + log_gdppc → Δreal HPI | 1556.1 | 0.188 | 54.9 | 0.963 | 0.009 | 732 |